graph in a rectangular coordinate x=3.5

Question

^ngle

Answer 1

What does  "graph in a rectangular coordinate x=3.5" really mean?
It asks you to do two things:
1)plot all the points which fulfill the requirement: X =3.5, Y can be any number
2) connect all those points  with a line.
Suppose you plot the following points on the rectangular coordinate, (3.5, 0), (3.5, 1) , (3.5, 2), (3.5, 5), then connect these points with a line. What will you see? you will find it is a vertical line, 3.5 units from y-axis.

Don't stop here , think about how to draw a line y=3.5
Same way, correct? Plot several points on a rectangular coordinate, then draw a line. This time, x can be any number, y is always 3.5.

 

Now, how is about 2x+3y=5?
It is same, find several points that fit for the equation 2x+3y=5 on the rectangular coordinate, then draw the line. You can choose any value for x and y that makes 2x+3y=5. Suppose you choose x=0, x=1, x=2, x=3. When x=0, 0+3y=5, so y=5/3; when x=1, 2+3y=5, so y=1; when x=2, 4+3y=5, so y=1/3; when x=3, 6+3y=5, so y=-1/3. Plot those points, then conncet them.

Now you will find those lines you just draw are all straight lines. Actually aX+bY=c is always a straight line.
When a=1, b=0, c=3.5, you get the equation x=3.5,
when a=0, b=1, c=3.5, you get the equation y=3.5
when a=2, b=3, c=5, you get the equation2x+3y=5

Rember a fact you only need to plot two points to draw a straight line. Hence, next time when you see that kind of equation, you only need to plot two points, then draw a line pass through these two points.

 

 

Answer 2

When graphign X=3.5

You:

(1) Find the X-axis (the horizontal line) and move exactly 3.5 units to the right.

(2) Draw a line vertically that passes through X = 3.5

Hint: The line will look like the Y-axis (vertical line), just shifted to the right.

Answer 3

It is a vertical line, 3.5 units from y-axis.